Problem: Reduce to lowest terms: $ \dfrac{9}{2} \div \dfrac{6}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{6}{5}$ is $ \dfrac{5}{6}$ Therefore: $ \dfrac{9}{2} \div \dfrac{6}{5} = \dfrac{9}{2} \times \dfrac{5}{6} $ $ \phantom{ \dfrac{9}{2} \times \dfrac{5}{6}} = \dfrac{9 \times 5}{2 \times 6} $ $ \phantom{ \dfrac{9}{2} \times \dfrac{5}{6}} = \dfrac{45}{12} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{45}{12} = \dfrac{45 \div 3}{12 \div 3} = \dfrac{15}{4} $